Free accessResearch articleFirst published online 2004-8
On the Equivalence of the Pseudophase Related Models and the Brönsted Approach in the Interpretation of Reactivity under Restricted Geometry Conditions
The equivalence of the Pseudophase and related models, frequently used in the interpretation of kinetic data under restricted geometry conditions, and the well known Brönsted's equation, used in the interpretation of the reactivity in homogeneous media, has been proven in several cases. The generalisation in relation to other non-kinetic properties such as reaction free energy and redox potentials has also been considered.
MengerF. M., and PortnoyC. E., J. Am. Chem. Soc., 1967, 89, 4698.
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LaidlerK. J., Chemical Kinetics, Mc Graw-Hill, New York, 1965, pp. 256 and f.f.
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HammesG. G., Thermodynamics and Kinetics for the Biological Sciences, Wiley-Interscience, New York, 2000, pp. 94 and f.f.
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In order to obtain Equation (3) from Equations (1) and (2) an additional hypothesis is necessary on the equilibrium distribution described by Equation (1): the concentration of the partitioned substrate must be low enough in order to avoid saturation of the dispersed (e.g., micellar) pseudophase. Indeed, even in this case, it is implicit that the presence of a substrate molecule in the dispersed pseudophase neither encourages nor discourages the union of a second molecule of substrate: in other words, binding of the substrate to the dispersed pseudophase is noncooperative in character. Moreover, to consider the binding constant and the rate constant characterizing reactivity in the dispersed phase as true constants, one must assume that some characteristics of this phase (for example the shape, size and charge of the micelles) are concentration independent parameters.
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Since transition states have a lifetime of about 10−13 s at ambient temperature, no exchange between a free and bound transition state is possible. However, it is possible to speak of equilibrium in the sense that, although an exchange is impossible, these transition state have the same chemical potential. In fact, equilibrium constant for the binding of transition states are well-documented (see for example HoukK. N., LeachA. G., KimS. P., and ZhangX., Angew. Chem. Int. Ed., 2003, 42, 4872 and references therein).
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Muriel-DelgadoF., JimenezR., Gomez-HerreraC., and SánchezF., Langmuir, 1999, 15, 4344.
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This state has been suggested as a convenient reference state for micellar solutions: N. Ise, T. Okubo and K. Shigern, Acc. Chems. Res., 1982, 15, 171. It is important to realize that, for these solutions the reference state of the solute is not the solute in the continuous phase (generally water) but the solute in the continuous phase in equilibrium with the micelles. These reference states are different because of the existence of monomers (or premicellar aggregates) in equilibrium with the micelles (see SanchezF., MoyáM. L., Gómez-HerreraC., CarmonaM. C., and López-CornejoP., J. Chem. Soc. Faraday. Trans., 1997, 93, 2181.
López-CornejoP., and SanchezF., J. Phys. Chem., 2001, 105, 10523.
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BuntonC. A., NomeF., QuinaF. M., and RomstedL. S., Acc. Chem. Res., 1991, 24, 357.
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In relation to Equations (79(a)) and (80(a)) it is relevant to note that kF is a second order rate constant and kB is a true first order rate constant, as follows from Equations (53) and (63) where these rate constants are defined.
